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1.
Multi-stage point and interval estimation of the largest mean ofK normal populations and the associated second-order properties 总被引:1,自引:0,他引:1
Summary We havek independent normal populations with unknown meansμ
1, …,μ
k and a common unknown varianceσ
2. Both point and interval estimation procedures for the largest mean are proposed by means of sequential and three-stage procedures.
For the point estimation problem, we require that the maximal risk be at mostW, a preassigned positive number. For the other problem, we wish to construct a fixed-width confidence interval having the
confidence coefficient at least 1-α, a preassigned number between zero and one. Asymptotic second order expansions are provided for various characteristics,
such as average sample size, associated risks etc., for the suggested multi-stage estimation procedures. 相似文献
2.
The problem of estimating a linear function of k normal means with unknown variances is considered under an asymmetric loss function such that the associated risk is bounded
from above by a known quantity. In the absence of a fixed sample size rule, sequential stopping rules satisfying a general
set of assumptions are considered. Two estimators are proposed and second-order asymptotic expansions of their risk functions
are derived. It is shown that the usual estimator, namely the linear function of the sample means, is asymptotically inadmissible,
being dominated by a shrinkage-type estimator. An example illustrates the use of different multistage sampling schemes and
provides asymptotic expansions of the risk functions.
Received: August 1999 相似文献
3.
Saibal Chattopadhyay 《Metrika》1998,48(1):53-59
The problem of estimating a normal mean with unknown variance is considered under an asymmetric loss function such that the
associated risk is bounded from above by a known quantity. In the absence of a fixed sample size rule, a sequential stopping
rule and two sequential estimators of the mean are proposed and second-order asymptotic expansions of their risk functions
are derived. It is demonstrated that the sample mean becomes asymptotically inadmissible, being dominated by a shrinkage-type
estimator. Also a shrinkage factor is incorporated in the stopping rule and similar inadmissibility results are established.
Received September 1997 相似文献
4.
N. Mukhopadhyay 《Metrika》1995,42(1):279-290
First the minimum risk point estimation as well as the fixed-width confidence interval problems for the mean parameter of a linear process are addressed under the framework of Fakhre-Zakeri and Lee (1992). The accelerated versions of their full sequential methodologies are introduced in order to achieve operational savings. Next, multi-sample analogs are discussed along the lines of Mukhopadhyay and Sriram (1992) both under full sequential as well as accelerated sequential sampling. In either setup, the first-order asymptotic characteristics are highlighted. 相似文献